Next, we discuss the way to share the kernel weight matrix \(\mathbf {W}_c\)  with multi-resolution data. Other than interpolating the kernel weight matrix as shown in (REF ) and (REF ), we propose another solution for the STFNet-convolution operation. The convolution operation concerns more about the pattern of relative positions on the frequency domain.
Therefore, instead of providing additional kernel details on fine-grained frequency resolution, we can just ensure that the convolution kernel is applied with the same frequency spacing on representations with different frequency resolutions.
Such idea can be implemented with the dilated convolution [1]}.
If \(\mathbf {W}_c\)  is applied to a input tensor with \(K=\lfloor \tau /2\rfloor +1\)  frequency components, for a input tensor with \(K^{\prime }=\lfloor \tau ^{\prime }/2\rfloor +1\)  frequency components (\(\tau ^{\prime } > \tau \) ), the dilated rate \(r\)  is set to \(\tau ^{\prime }/\tau - 1\) .
A simple illustration of STFNet-convolution with dilated configuration is shown in Figure REF .
